Audio drop box is what you are looking for. I just tested and it is worth giving it a try. you have to create an account at CLEAR, from Michigan State University, create your audio drop box. Voilà! You are ready to go! You can even create different audio drop boxes for different groups.
"an Audio Dropbox is a virtual dropbox for audio recordings. Using this new tool, you can put a dropbox for speaking assignments on any web page.From within that web page, students record themselves, and their audio files are automatically put into your dropbox.You can access your dropbox from anywhere and listen to the recordings. Put a dropbox on your home page, mashup, wiki, or blog. Using this tool is as easy as copying and pasting. You don't have to upload or download anything, and it works on any computer from anywhere."
I recommend it!